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arXiv:cond-mat/0608484 · New Journal of Physics

Dissipative quantum oscillator with two competing heat baths

Heiner Kohler, Fernando Sols

Published Aug 25, 2006• 21 citations
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Abstract

We study the dissipative dynamics of a harmonic oscillator which couples linearly through its position and its momentum to two independent heat baths at the same temperature. We argue that this model describes a large spin in a ferromagnet. We find that some effects of the two heat baths partially cancel each other. This leads to unexpected features such as underdamped oscillations and long relaxation times in the strong coupling regime. Such a partial frustration of dissipation can be ascribed to the canonically conjugate character of position and momentum. We compare this model to the scenario where a single heat bath couples linearly to both the position and the momentum of the central oscillator. In that case less surprising behaviour occurs for strong coupling. The dynamical evolution of the quantum purity for a single and a double wave packet is also investigated.

DOI
10.1088/1367-2630/8/8/149

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We study the dissipative dynamics of a harmonic oscillator which couples linearly through its position and its momentum to two independent heat baths at the same temperature. We argue that this model describes a large spin in a ferromagnet. We find that some effects of the two heat baths partially cancel each other. This leads to unexpected features such as underdamped oscillations and long relaxation times in the strong coupling regime. Such a partial frustration of dissipation can be ascribed to the canonically conjugate character of position and momentum. We compare this model to the scenario where a single heat bath couples linearly to both the position and the momentum of the central oscillator. In that case less surprising behaviour occurs for strong coupling. The dynamical evolution of the quantum purity for a single and a double wave packet is also investigated.
We study the dissipative properties of a harmonic oscillator subject to two independent heat baths, one of which couples to its position and the other one to its momentum. This model describes a large spin impurity in a ferromagnet. We find that some effects of the two heat baths partially cancel each other. Most notably, oscillations may remain underdamped for arbitrarily strong coupling. This effect is a direct consequence of the mutually conjugate character of position and momentum. For a single dissipative bath coupled linearly to both position and momentum, no underdamped regime is possible for strong coupling. The dynamics of purity loss for one and two wave packets is also investigated.
We study a quantum harmonic oscillator linearly coupled through the position operator to a first bath and through the momentum operator to a second bath yielding an Ohmic–Drude dissipation. We analyse the oscillator's fluctuations as a function of the ratio between the strength of the two couplings, focusing in particular on the situation in which the two dissipative interactions are comparable. Analytic formulas are derived in the relevant regimes corresponding to the low temperature limit and when the Drude high frequency cutoff is much larger than all other frequencies. At low temperature, each bath operates to suppress the oscillator's ground state quantum fluctuations or appearing in the corresponding interaction. When one of the two dissipative interactions dominates over the other, the fluctuations for the coupling operator are squeezed. When the two interactions are comparable, the two baths enter in competition as the two conjugate operators do not commute yielding quantum frustration . In this regime, remarkably, the fluctuations of both two quadratures can be enhanced by increasing the dissipative coupling.
We investigate the evolution of a central spin coupled to a spin bath without internal dynamics. We compare the cases where the bath couples to one or two components of the spin. It is found that the central spin dynamics is enhanced in the latter case, which may be interpreted as a frustration of dissipation. However, the quantum purity of the spin decays fast in both scenarios. We conclude that symmetric coupling of the bath to two orthogonal components of the spin inhibits dissipation but not decoherence.
We consider the problem of a single quantum oscillator coupled linearly to a heat bath of independent harmonic modes. An exact solution is presented for the system-oscillator observables of interest. The exact results are then used to evaluate the utility of a variational approach to the problem that has proven useful recently in elucidating the dynamics of dissipatively coupled systems. We find that the variational approach does provide a good description for most, but not all, observables of interest. Both the exact and the variational treatment demonstrate the important role played by the low-frequency bath modes in determining qualitative features of the dynamical behavior.
We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four ``canonical'' system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems and micron-scale ion traps. Decoherence and dissipation rates are found to exhibit temperature dependencies significantly different from those in quantum Brownian motion. In particular, the systematic dissipation rate for the central oscillator decreases with increasing temperature and goes to zero at zero temperature, but there also exists a temperature-independent momentum-diffusion (heating) rate.